A number of recently developed microelectronic package designs consist of a relatively thick molded plastic, typically thermosetting epoxy molding compounds, encapsulating integrated circuits or other devices on one side of a thin insulating substrate. This substrate, which can be a ceramic, an epoxy glass, or some other insulating material is prone to failure because of the elevated bending stresses caused by thermal expansion mismatch between the molded plastic layer and the substrate in the package. The stress-free state of a molded device is typically at or close m the molding temperature, (usually in the range of 170.degree.-180.degree. C). During the subsequent cooling of the package to room temperature, thermally induced bending stresses occur in the package. These resulting elevated bending stresses, which may lead to bowing or cracking of the substrate, are undesirable. An immediate postbaking operation at the molding temperature of the package taken directly from the mold may not be sufficient in reducing the bending stresses to a safe level eliminating bowing. Appreciable thermally induced bowing and high thermal stresses occur even in conventional ball grid array (BGA) packages which typically utilize FR4 or BT epoxy glass substrate materials with coefficients of thermal expansion close to those of epoxy molding compounds. Accordingly, there is a need for a packaging arrangement which reduces bending stress.